The Portuguese manager signed a contract extension only in January, but after a frustrating transfer window in which he was not allowed to sign a centre-back such as Harry Maguire, tensions have increased at the club.
Man Utd also fell to a disappointing 3-1 defeat away to Brighton, which has added extra pressure on the manager's shoulders after his team performed so poorly in the game.
Despite there being rumours that former Real Madrid boss Zinedine Zidane is being lined up to replace Mourinho, a senior official at the club is quoted as giving his backing to the current manager.
The 'Daily Mail' report the representative as saying "Why would we discuss him when there is no job available?" when asked about Mourinho's future.
The Man Utd boss will hope to get his side back to winning ways when they play Tottenham at home next weekend.